Electric Field, Potential, Capacitance & Current Notes
Chapter 1: Electric Field and Dipole
Electric Field
Electric field: The sphere around a source charge in which a test charge would experience a force is called the electric field.
Electric Field Lines
Electric field lines: An electric field is represented by imaginary lines of force which are called electric field lines.
Properties
- They are imaginary lines of force.
- In the case of a positive source charge they are radially directed outward.
- They are not closed lines.
Mathematical Definition of Electric Field
Mathematically defined: The electric force per unit test charge is called the electric field.
i.e. E = F / q0. SI unit: newton per coulomb (N/C).
Electric Dipole
Electric dipole: An electric dipole consists of two dissimilar charges having equal magnitude separated by a small distance.
Electric Dipole Moment
Electric dipole moment: It is equal to the product of the magnitude of either charge and the dipole length.
i.e. p = q × 2l. SI unit: coulomb metre (C·m).
Ideal Dipole
Ideal dipole: An electric dipole is said to be ideal if it has infinite field strength and the dipole length tends to zero (2l = 0).
Electric Flux
Electric flux: The number of electric field lines passing through a surface normally is called electric flux.
Gauss’s Law of Electrostatics
Gauss’s law: The total electric flux linked with a closed surface is equal to 1/ε0 times the total charge enclosed by the surface.
Mathematically: ∫ E · dA = Qenc / ε0.
Chapter 2: Electric Potential and Capacitance
Electric Potential (V)
Electric potential (V): Electric potential at a point inside an electric field is defined as the amount of work done in bringing a unit positive test charge from infinity to that point.
i.e. V = W / q0. SI unit: volt (V).
Electric Potential Difference
Electric potential difference: The potential difference (PD) between two points inside an electric field is defined as the amount of work done in displacing a unit positive test charge from the point of lower potential to the point of higher potential.
Potential at A = VA (low), potential at P = VP (high).
PD between the two points: V = VP – VA = W / q0. SI unit: volt (V).
Equipotential Surface
Equation of equipotential surface: Equipotential surfaces give a visual picture of both the direction and the magnitude of the electric field in a region of space. If we draw equipotential surfaces at regular intervals of V, we find that the equipotential surfaces are closer together in regions of strong field and farther apart in regions of weak electric field.
Capacitance
Capacitance (or capacitor): Charge stored in a capacitor is directly proportional to the potential difference applied across the capacitor.
i.e. Q is directly proportional to V. SI unit: farad (F).
Chapter 3: Electric Current and Resistance
Electric Current
Electric current: The rate of flow of charge through a conductor is called electric current.
Mathematically: I = q / t. SI unit: ampere (A).
Conventional Current
Conventional current: By convention, the direction of flow of a positive charge through a conductor is the direction of conventional current, which is opposite to the direction of flow of electrons.
Potential Difference in a Conductor
Potential difference: The potential difference (PD) between two points in a current-carrying conductor is defined as the amount of work done in displacing a unit charge from one point to another.
V = W / Q. SI unit: volt (V).
Ohm’s Law of Electrostatics
Ohm’s law: At constant temperature, the potential difference applied across a conductor is directly proportional to the current flowing through it.
V is directly proportional to I, V = R I. SI unit of resistance: ohm (Ω).
Specific Resistance (Resistivity)
Specific resistance or resistivity (ρ): The resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area.
i.e. R ∝ L and R ∝ 1 / A.
Combining: R ∝ L / A, therefore R = ρ × L / A. SI unit: ohm metre (Ω·m).